Probabilistic Recursively Feasible Motion Planning Under Uncertain Environments
For autonomous systems operating in dynamic environments, this work provides a probabilistic guarantee of recursive feasibility, addressing a key limitation in existing MPC-based motion planning.
The paper tackles safe motion planning in uncertain, time-varying environments where recursive feasibility is often lost. The proposed PRF-MPC framework guarantees recursive feasibility with a specified probability, demonstrated via simulations on a lane-change scenario.
Safe motion planning in uncertain, time-varying environments is challenging because the safe region can change unpredictably across planning steps, often causing a loss of recursive feasibility. In this work, we present a Probabilistic Recursively Feasible Model Predictive Control (PRF-MPC) framework that guarantees recursive feasibility with a specified probability. We introduce properties that an ideal predictor should satisfy to ensure distributional consistency, and use these properties to derive closed-form expressions for the means and covariances of trajectories predicted at future time steps. Building on this analysis, we construct safety constraints that ensure, with high probability, that the current safe set is contained within the safe sets at future time steps, thereby probabilistically guaranteeing recursive feasibility. Simulation results on a lane-change scenario demonstrate that the proposed method significantly improves recursive feasibility.